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So, R. M. C.

Publications and source records attributed to So, R. M. C..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Zhao, C. Y.↗
NASA NTRS1999

Predicting Buoyant Shear Flows Using Anisotropic Dissipation Rate Models

This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated-, the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered: one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of' the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows. pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.

So, R. M. C.↗
NASA NTRS1997

A Near-Wall Reynolds-Stress Closure Without Wall Normals

Turbulent wall-bounded complex flows are commonly encountered in engineering practice and are of considerable interest in a variety of industrial applications. The presence of a wall significantly affects turbulence characteristics. In addition to the wall effects, turbulent wall-bounded flows become more complicated by the presence of additional body forces (e.g. centrifugal force and Coriolis force) and complex geometry. Most near-wall Reynolds stress models are developed from a high-Reynolds-number model which assumes turbulence is homogenous (or quasi-homogenous). Near-wall modifications are proposed to include wall effects in near-wall regions. In this process, wall normals are introduced. Good predictions could be obtained by Reynolds stress models with wall normals. However, ambiguity arises when the models are applied in flows with multiple walls. Many models have been proposed to model turbulent flows. Among them, Reynolds stress models, in which turbulent stresses are obtained by solving the Reynolds stress transport equations, have been proved to be the most successful ones. To apply the Reynolds stress models to wall-bounded flows, near-wall corrections accounting for the wall effects are needed, and the resulting models are called near-wall Reynolds stress models. In most of the existing near-wall models, the near-wall corrections invoke wall normals. These wall-dependent near-wall models are difficult to implement for turbulent flows with complex geometry and may give inaccurate predictions due to the ambiguity of wall normals at corners connecting multiple walls. The objective of this study is to develop a more general and flexible near-wall Reynolds stress model without using any wall-dependent variable for wall-bounded turbulent flows. With the aid of near-wall asymptotic analysis and results of direct numerical simulation, a new near-wall Reynolds stress model (NNWRS) is formulated based on Speziale et al.'s high-Reynolds-stress model with wall-independent near-wall corrections. Moreover, only one damping function is used for flows with a wide range of Reynolds numbers to ensure that the near-wall modifications diminish away from the walls.

Yuan, S. P.↗
NASA NTRS1997

A Near-Wall Reynolds-Stress Closure without Wall Normals

With the aid of near-wall asymptotic analysis and results of direct numerical simulation, a new near-wall Reynolds stress model (NNWRS) is formulated based on the SSG high-Reynolds-stress model with wall-independent near-wall corrections. Only one damping function is used for flows with a wide range of Reynolds numbers to ensure that the near-wall modifications diminish away from the walls. The model is able to reproduce complicated flow phenomena induced by complex geometry, such as flow recirculation, reattachment and boundary-layer redevelopment in backward-facing step flow and secondary flow in three-dimensional square duct flow. In simple flows, including fully developed channel/pipe flow, Couette flow and boundary-layer flow, the wall effects are dominant, and the NNWRS model predicts less degree of turbulent anisotropy in the near-wall region compared with a wall-dependent near-wall Reynolds Stress model (NWRS) developed by So and colleagues. The comparison of the predictions given by the two models rectifies the misconception that the overshooting of skin friction coefficient in backward-facing step flow prevalent in those near-wall, models with wall normal is caused by he use of wall normal.

Yuan, S. P.↗
NASA NTRS1994

Development of a near-wall Reynolds-stress closure based on the SSG model for the pressure strain

In this research, a near-wall second-order closure based on the Speziable et al.(1991) or SSG model for the pressure-strain term is proposed. Unlike the LRR model, the SSG model is quasi-nonlinear and yields better results when applied to calculate rotating homogeneous turbulent flows. An asymptotic analysis near the wall is applied to both the exact and modeled, equations so that appropriate near-wall corrections to the SSG model and the modeled dissipation-rate equation can be derived to satisfy the physical wall boundary conditions as well as the asymptotic near-wall behavior of the exact equations. Two additional model constants are introduced and they are determined by calibrating against one set of near-wall channel flow data. Once determined, their values are found to remain constant irrespective of the type of flow examined. The resultant model is used to calculate simple turbulent flows, near separating turbulent flows, complex turbulent flows and compressible turbulent flows with a freestream Mach number as high as 10. In all the flow cases investigated, the calculated results are in good agreement with data. This new near-wall model is less ad hoc, physically and mathematically more sound and eliminates the empiricism introduced by Zhang. Therefore, it is quite general, as demonstrated by the good agreement achieved with measurements covering a wide range of Reynolds numbers and Mach numbers.

So, R. M. C.↗
NASA NTRS1993

Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model

A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.

Sommer, T. P.↗
NASA NTRS1993

On the assumption of vanishing temperature fluctuations at the wall for heat transfer modeling

Boundary conditions for fluctuating wall temperature are required for near-wall heat transfer modeling. However, their correct specifications for arbitrary thermal boundary conditions are not clear. The conventional approach is to assume zero fluctuating wall temperature or zero gradient for the temperature variance at the wall. These are idealized specifications and the latter condition could lead to an ill posed problem for fully-developed pipe and channel flows. In this paper, the validity and extent of the zero fluctuating wall temperature condition for heat transfer calculations is examined. The approach taken is to assume a Taylor expansion in the wall normal coordinate for the fluctuating temperature that is general enough to account for both zero and non-zero value at the wall. Turbulent conductivity is calculated from the temperature variance and its dissipation rate. Heat transfer calculations assuming both zero and non-zero fluctuating wall temperature reveal that the zero fluctuating wall temperature assumption is in general valid. The effects of non-zero fluctuating wall temperature are limited only to a very small region near the wall.

Sommer, T. P.↗
NASA NTRS1993

Near-wall variable-Prandtl-number turbulence model for compressible flows

A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon (sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, there are significant improvements in the predictions of mean flow properties at high Mach numbers.

Sommer, T. P.↗
NASA NTRS1992

A near-wall two-equation model for turbulent heat fluxes

A near-wall two-equation model for turbulent heat fluxes is derived from the temperature variance and its dissipation-rate equations and the assumption of gradient transport. Only incompressible flows with non-buoyant heat transfer are considered. The near-wall asymptotics of each term in the exact equations are examined and used to derive near-wall correction functions that render the modeled equations consistent with these behavior. Thus modeled, the equations are used to calculate fully-developed pipe and channel flows with heat transfer. It is found that the proposed two-equation model yields asymptotically correct near-wall behavior for the normal heat flux, the temperature variance and its near-wall budget and correct limiting wall values for these properties compared to direct simulation data and measurements obtained under different wall boundary conditions.

Sommer, T. P.↗
NASA NTRS1992

On the prediction of turbulent secondary flows

The prediction of turbulent secondary flows, with Reynolds stress models, in circular pipes and non-circular ducts is reviewed. Turbulence-driven secondary flows in straight non-circular ducts are considered along with turbulent secondary flows in pipes and ducts that arise from curvature or a system rotation. The physical mechanisms that generate these different kinds of secondary flows are outlined and the level of turbulence closure required to properly compute each type is discussed in detail. Illustrative computations of a variety of different secondary flows obtained from two-equation turbulence models and second-order closures are provided to amplify these points.

Speziale, C. G.↗
NASA NTRS1992

A near-wall four-equation turbulence model for compressible boundary layers

A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon(sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, the numerical predictions are in very good agreement with measurements and there are significant improvements in the predictions of mean flow properties at high Mach numbers.

Sommer, T. P.↗
NASA NTRS1992

A near-wall two-equation model for compressible turbulent flows

A near-wall two-equation turbulence model of the k-epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K-omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.

Zhang, H. S.↗
NASA NTRS1992

A compressible near-wall turbulence model for boundary layer calculations

A compressible near-wall two-equation model is derived by relaxing the assumption of dynamical field similarity between compressible and incompressible flows. This requires justifications for extending the incompressible models to compressible flows and the formulation of the turbulent kinetic energy equation in a form similar to its incompressible counterpart. As a result, the compressible dissipation function has to be split into a solenoidal part, which is not sensitive to changes of compressibility indicators, and a dilational part, which is directly affected by these changes. This approach isolates terms with explicit dependence on compressibility so that they can be modeled accordingly. An equation that governs the transport of the solenoidal dissipation rate with additional terms that are explicitly dependent on the compressibility effects is derived similarly. A model with an explicit dependence on the turbulent Mach number is proposed for the dilational dissipation rate. Thus formulated, all near-wall incompressible flow models could be expressed in terms of the solenoidal dissipation rate and straight-forwardly extended to compressible flows. Therefore, the incompressible equations are recovered correctly in the limit of constant density. The two-equation model and the assumption of constant turbulent Prandtl number are used to calculate compressible boundary layers on a flat plate with different wall thermal boundary conditions and free-stream Mach numbers. The calculated results, including the near-wall distributions of turbulence statistics and their limiting behavior, are in good agreement with measurements. In particular, the near-wall asymptotic properties are found to be consistent with incompressible behavior; thus suggesting that turbulent flows in the viscous sublayer are not much affected by compressibility effects.

So, R. M. C.↗
NASA NTRS1991

Near-wall modeling of the dissipation rate equation

Near-wall modeling of the dissipation rate equation is investigated and its asymptotic behavior is studied in detail using a k-epsilon model. It is found that all existing modeled dissipation rate equations predict an incorrect behavior for the dissipation rate near a wall. An improvement is proposed and the resulting near-wall dissipation rate distribution is found to be similar to that given by numerical simulation data. To further validate the improved k-epsilon model, it is used to calculate flat-plate turbulent boundary-layer flows at high- as well as low-turbulence Reynolds numbers, and the results are compared with measurements, numerical simulation data, and the calculations of three different two-equation models. These comparisons show that all the models tested give essentially the same flow properties away from the wall; significant differences only occur in a region very close to the wall. In this region, the calculations of the improved k-epsilon model are in better agreement with measurements and numerical simulation data. In particular, the modeled distribution of the dissipation rate is significantly improved and a maximum is predicted at the wall instead of away from the wall. Furthermore, the improved k-epsilon model is found to be the most asymptotically consistent among the four different two-equation models examined.

So, R. M. C.↗
NASA NTRS1991

A near-wall two-equation model for compressible turbulent flows

A near-wall two-equation turbulence model of the K - epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K - omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.

Zhang, H. S.↗
NASA NTRS1991

Second-order near-wall turbulence closures - A review

Advances in second-order near-wall turbulence closures are summarized. All closures under consideration are based on high-Reynolds-number models. Most near-wall closures proposed to date attempt to modify the high-Reynolds-number models for the dissipation function and the pressure redistribution term so that the resultant models are applicable all the way to the wall. The asymptotic behavior of the near-wall closures is examined and compared with the proper near-wall behavior of the exact Reynolds-stress equations. It is found that three second-order near-wall closures give the best correlations with simulated turbulence statistics. However, their predictions of near-wall Reynolds-stress budgets are considered to be incorrect. A proposed modification to the dissipitation-rate equation remedies part of those predictions. It is concluded that further improvements are required if a complete replication of all the turbulence properties and Reynolds-stress budgets by a statistical model of turbulence is desirable.

So, R. M. C.↗
NASA NTRS1991

Near-wall turbine closure for curved flows

At present, turbulence closures for curved flows only account for curvature effects in the fully turbulent region where the Reynolds number is large. The justification is that, near a wall, viscous effects dominate and curvature effects are only of secondary importance. Recent direct simulation data show that this assumption is not valid, even for simple two-dimensional fully developed turbulent curved channel flows. This paper presents an approach to develop a near-wall turbulence closure for wall-bounded curved flows. The curved channel direct simulation data is used as a guide to held develop such a closure. The proposed closure has the unique property of approaching conventional high-Reynolds-number Reynolds-stress closures far away from the wall. Hence, curvature effects in both the near-wall and the fully turbulent parts of the flow are accounted for properly. Validations of the closure are carried out with a set of low-Reynolds-number simulation data and with experimental measurements at high Reynolds number. Good agreement is obtained in both cases; in particular, the anisotropic behavior of the normal stresses and the shear stress behavior near the convex and concave walls.

So, R. M. C.↗